please solve all parts (a) For which values of r e R is the sequence x, divergent

please solve all parts 

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(a) For which values of r e R is the sequence x, divergent or convergent? What could the limit be ? , n e N (4 marks) (b) Find the values of a, b so that the function below is continuous: |3x – 4|, r E [0, 1) f : R → R, f(x) = ax, x = 1 x2 + 2x + b, x > 1. (4 marks) (c) Prove that the function f : R→ R defined by f(x) = 4x? – 4x – 3 has roots in the intervals [1, 2] and [-1,0]. %3D | (4 marks) (d) Find the number of real roots of the function f : R → R below. f(x) = 8x – 4.x? – 18x + 9 (4 marks) (e) Find the critical points and their nature for f : R R above. (4 marks) (a) For which values of r e R is the sequence x, divergent or convergent? What could the limit be ? , n e N (4 marks) (b) Find the values of a, b so that the function below is continuous: |3x – 4|, r E [0, 1) f : R → R, f(x) = ax, x = 1 x2 + 2x + b, x > 1. (4 marks) (c) Prove that the function f : R→ R defined by f(x) = 4x? – 4x – 3 has roots in the intervals [1, 2] and [-1,0]. %3D | (4 marks) (d) Find the number of real roots of the function f : R → R below. f(x) = 8x – 4.x? – 18x + 9 (4 marks) (e) Find the critical points and their nature for f : R R above. (4 marks)